Numerical analysis and simulations of a dynamic frictionless contact problem with damage

Campo, M.; Fernández, José R.; Kuttler, Kenneth; Shillor, Meir; Viaño, J. M.

doi:10.1016/j.cma.2006.05.006

Cited by 99 publications

(76 citation statements)

References 17 publications

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“…Combination with viscosity has been addressed in the Maxwellian rheology (even with plasticity) in [16] and in the Kelvin-Voigt rheology in [25,43,49,10].…”

Section: Damage In Viscoelastic Media With Inertiamentioning

confidence: 99%

Complete damage in elastic and viscoelastic media and its energetics

Mielke

Roubíček

Zeman

2010

Computer Methods in Applied Mechanics and Engineering

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“…Combination with viscosity has been addressed in the Maxwellian rheology (even with plasticity) in [16] and in the Kelvin-Voigt rheology in [25,43,49,10].…”

Section: Damage In Viscoelastic Media With Inertiamentioning

confidence: 99%

Complete damage in elastic and viscoelastic media and its energetics

Mielke

Roubíček

Zeman

2010

Computer Methods in Applied Mechanics and Engineering

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“…Moreover, recently these kinds of materials have been considered in contact problems (see [12] and the references cited therein for the quasistatic case or, for example, [5] for the dynamical one).…”

Section: Introductionmentioning

confidence: 99%

A priori and a posteriori error analyses in the study of viscoelastic problems

Fernández

Hild

2009

Journal of Computational and Applied Mathematics

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International audienceIn this work, the numerical approximation of a viscoelastic problem is studied. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. Then, two numerical analyses are presented. First, a priori estimates are proved from which the linear convergence of the algorithm is derived under suitable regularity conditions. Secondly, an a posteriori error analysis is provided extending some preliminary results obtained in the study of the heat equation. Upper and lower error bounds are obtained

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“…To obtain a heat conduction theory with delays but without such an explosive behaviour, Quintanilla combined the delay parameters of Tzou with the two‐temperatures theory proposed by Chen and Gurtin and Warren and Chen . The basic constitutive equation reads

q_{i} (x, t + τ_{1}) = - k_{2} T_{, i} (x, t + τ_{2}),

where θ = T − a Δ T , being T and a the inductive temperature and a positive constant, respectively.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of a dual‐phase‐lag model involving two temperatures

Bazarra

Fernández

Magaña

et al. 2019

Math Methods in App Sciences

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In this paper, we numerically analyse a phase‐lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one‐dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution.

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Numerical analysis and simulations of a dynamic frictionless contact problem with damage

Cited by 99 publications

References 17 publications

Complete damage in elastic and viscoelastic media and its energetics

Complete damage in elastic and viscoelastic media and its energetics

A priori and a posteriori error analyses in the study of viscoelastic problems

Numerical analysis of a dual‐phase‐lag model involving two temperatures

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